text: Heat is thermal energy associated with temperature-dependent motion of particles. The macroscopic energy equation for infinitesimal volume used in heat transfer analysis is
  where  is heat flux vector,  is temporal change of internal energy ( is density,  is specific heat capacity at constant pressure,  is temperature and  is time), and  is the energy conversion to and from thermal energy ( and  are for principal energy carriers). So, the terms represent energy transport, storage and transformation.  Heat flux vector  is composed of three macroscopic fundamental modes, which are conduction (, : thermal conductivity), convection (, : velocity), and radiation (, : angular frequency, : polar angle, : spectral, directional radiation intensity, : unit vector), i.e., .
  Once states and kinetics of the energy conversion and thermophysical properties are known, the fate of heat transfer is described by the above equation. These atomic-level mechanisms and kinetics are addressed in heat transfer physics. The microscopic thermal energy is stored, transported, and transformed by the principal energy carriers: phonons (p), electrons (e), fluid particles (f), and photons (ph).